Crane Cams Article-Valve Spring Resonance: What it is and how it can be controlled!
Best description I could find that describes the function and application of the valve spring coil dampener. Here is the only advantage of the flat wound spring dampener as described in the article;
"One real plus of a damper used with a (single) coil spring is that if the spring should break, the damper acts as a safety to keep pressure on the retainer/lock package to prevent dropping the valve into the cylinder."
Kind of explains why they started using them on very early engines with poor quality spring wire, they would occasionally break and this was a safety device. Most engines today (except for heavy duty diesels) don't use them as the engine speed is never constant and loads on the engine isn't high enough which could cause spring surge situations.